Two-dimensional Turing-like patterns in the PA-MBO-System and effects of an electric field

Münster, Arno F.; Watzl, M; Schneider, F. W.

doi:10.1088/0031-8949/1996/t67/011

Cited by 18 publications

(16 citation statements)

References 29 publications

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“…A variety of interesting phenomena have been discovered [Ouyang et al, 1992;Perraud et al, 1993;Rudovics et al, 1996], and similar patterns have been obtained in other chemical reactions [Münster et al, 1996].…”

Section: Introductionsupporting

confidence: 64%

Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction

Mosekilde

Larsen

Dewel

et al. 1998

Int. J. Bifurcation Chaos

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Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction-diffusion systems are studied through numerical simulation of the Lengyel-Epstein model. By varying the feed concentrations, a transition is observed in which hexagons are replaced by stripes and these again by inverted hexagons. The competition between Hopf oscillations and Turing stripes is investigated by following the propagation of a front connecting the two modes. In certain parameter regimes, mode-locking is found to occur. The front then moves an integer number of Turing stripes during an integer number of Hopf oscillations. This phenomenon can be seen as arising from depinning of the Turing front under influence of the Hopf mode.

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Section: Introductionsupporting

confidence: 64%

Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction

Mosekilde

Larsen

Dewel

et al. 1998

Int. J. Bifurcation Chaos

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“…[7][8][9] Here, we show that patterns similar but not identical to TS arise during the polymerization of acrylamide in the presence of sulfide alone.…”

Section: Introductionmentioning

confidence: 58%

“…All stock solutions but (NH 4 ) 2 S 2 O 8 and Na 2 S could be stored for extended periods of time without decomposition. The following stock solutions were made: [ 3 ), gelation takes about 10 min, 20 min, and 3-4 h or 5, 10, and 40-50 min, respectively.…”

Section: Methodsmentioning

confidence: 99%

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Pattern Formation during Polymerization of Acrylamide in the Presence of Sulfide Ions

1998

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When polyacrylamide gel is prepared from a mixture of acrylamide, N,N′-methylene-bisacrylamide and triethanolamine with a peroxodisulfate initiator in the presence of sulfide, spatial pattern formation occurs in the gel if water is spread on top of the gel after it solidifies. These patterns, typically arrays of spots or stripes, persist for many hours. Analysis of the effects of temperature, composition, stirring, and other factors suggests that the pattern formation occurs during polymerization due to convection driven by the highly exothermic polymerization reaction. The role of sulfide ion, which is essential for the pattern formation, appears to be to terminate the polymer chain elongation while maintaining the overall exothermic chain reaction.

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“…Examples include thin copolymer films that have already been analyzed using scalar Minkowski functionals (Rehse et al, 2008). An analysis using tensorial Minkowski functionals will be of genuine benefit when considering such systems under the influence of aligning fields, such as the experiments reported in Olszowka et al (2006) for diblock copolymers or for Turing patterns in Münster et al (1996).…”

Section: Application: Local Alignment In Turing Patternsmentioning

confidence: 99%

Tensorial Minkowski functionals and anisotropy measures for planar patterns

Schröder‐Turk

Kapfer

Breidenbach

et al. 2010

Journal of Microscopy

144

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SummaryQuantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor-valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non-equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores.

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Two-dimensional Turing-like patterns in the PA-MBO-System and effects of an electric field

Cited by 18 publications

References 29 publications

Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction

Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction

Pattern Formation during Polymerization of Acrylamide in the Presence of Sulfide Ions

Tensorial Minkowski functionals and anisotropy measures for planar patterns

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